6533b7d0fe1ef96bd125acfd

RESEARCH PRODUCT

Nucleon isovector charges and twist-2 matrix elements with Nf=2+1 dynamical Wilson quarks

subject

description

We present results from a lattice QCD study of nucleon matrix elements at vanishing momentum transfer for local and twist-2 isovector operator insertions. Computations are performed on gauge ensembles with nonperturbatively improved ${N}_{f}=2+1$ Wilson fermions, covering four values of the lattice spacing and pion masses down to ${M}_{\ensuremath{\pi}}\ensuremath{\approx}200\text{ }\text{ }\mathrm{MeV}$. Several source-sink separations (typically $\ensuremath{\sim}1.0$ to $\ensuremath{\sim}1.5\text{ }\text{ }\mathrm{fm}$) allow us to assess excited-state contamination. Results on individual ensembles are obtained from simultaneous two-state fits across all observables and all available source-sink separations with the energy gap as a common fit parameter. Renormalization has been performed nonperturbatively using the Rome-Southampton method for all but the finest lattice spacing for which an extrapolation has been used. Physical results are quoted in the $\overline{\mathrm{MS}}$ scheme at a scale of $\ensuremath{\mu}=2\text{ }\text{ }\mathrm{GeV}$ and are obtained from a combined chiral, continuum, and finite-size extrapolation. For the nucleon isovector axial, scalar, and tensor charges we find physical values of ${g}_{A}^{u\ensuremath{-}d}=1.242(25{)}_{\mathrm{stat}}(\genfrac{}{}{0ex}{}{+00}{\ensuremath{-}31}{)}_{\mathrm{sys}}$, ${g}_{S}^{u\ensuremath{-}d}=1.13(11{)}_{\mathrm{stat}}(\genfrac{}{}{0ex}{}{+07}{\ensuremath{-}06}{)}_{\mathrm{sys}}$ and ${g}_{T}^{u\ensuremath{-}d}=0.965(38{)}_{\mathrm{stat}}(\genfrac{}{}{0ex}{}{+13}{\ensuremath{-}41}{)}_{\mathrm{sys}}$, respectively, where individual systematic errors in each direction from the chiral, continuum, and finite-size extrapolation have been added in quadrature. Our final results for the isovector average quark momentum fraction and the isovector helicity and transversity moments are given by $⟨x{⟩}_{u\ensuremath{-}d}=0.180(25{)}_{\mathrm{stat}}(\genfrac{}{}{0ex}{}{+14}{\ensuremath{-}06}{)}_{\mathrm{sys}}$, $⟨x{⟩}_{\mathrm{\ensuremath{\Delta}}u\ensuremath{-}\mathrm{\ensuremath{\Delta}}d}=0.221(25{)}_{\mathrm{stat}}(\genfrac{}{}{0ex}{}{+10}{\ensuremath{-}00}{)}_{\mathrm{sys}}$, and $⟨x{⟩}_{\ensuremath{\delta}u\ensuremath{-}\ensuremath{\delta}d}=0.212(32{)}_{\mathrm{stat}}(\genfrac{}{}{0ex}{}{+20}{\ensuremath{-}10}{)}_{\mathrm{sys}}$, respectively.